x° = 43°
Solution:
The lines AD, BE and CF are intersecting lines.
Given m∠AGF = 47°, m∠BGC = 90°, m∠DGE = x°.
To find the value of x°:
Line BE and line CF intersect at the vertex G.
∠BGC and ∠FGE are vertical angles.
Vertical angle theorem:
If two angles are vertically opposite then they are congruent.
By vertical angle theorem, ∠BGC ≅ ∠FGE
⇒ m∠FGE = 90°
Sum of the angles in a straight line = 180°
In line AD,
m∠AGF + m∠FGE + m∠DGE = 180°
⇒ 47° + 90° + m∠DGE = 180°
⇒ 137° + m∠DGE = 180°
⇒ m∠DGE = 180° – 137°
⇒ m∠DGE = 43°
⇒ x° = 43°
Hence the value of x° is 43°.
